Simplify the following expression: $q = \dfrac{6}{2p + 9} \div \dfrac{6}{10p}$
Dividing by an expression is the same as multiplying by its inverse. $q = \dfrac{6}{2p + 9} \times \dfrac{10p}{6}$ When multiplying fractions, we multiply the numerators and the denominators. $q = \dfrac{ 6 \times 10p } { (2p + 9) \times 6}$ $q = \dfrac{60p}{12p + 54}$ Simplify: $q = \dfrac{10p}{2p + 9}$